1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a study to detect a statistically significant effect. It depends on the confidence level, margin of error, and expected proportion in the population.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( Z \) — Z-score for desired confidence level
• \( p \) — Estimated proportion (0.5 if unknown)
• \( e \) — Margin of error (e.g., 0.05 for ±5%)

For finite populations, we apply the correction: \[ n_{adj} = \frac{n}{1 + \frac{(n - 1)}{N}} \] where \( N \) is the population size.

3. Importance of Sample Size

Details: Proper sample size ensures studies have adequate power to detect effects while avoiding unnecessary costs from oversized samples. It's crucial for study design and statistical validity.

4. Using the Calculator

Tips:

• Use 0.5 for proportion when uncertain (maximizes required sample size)
• Common margins are 0.05 (±5%) or 0.03 (±3%)
• Include population size only when sampling from a small finite group

5. Frequently Asked Questions (FAQ)

Q1: Why is 0.5 used when proportion is unknown?
A: 0.5 gives the most conservative (largest) sample size since p(1-p) is maximized at p=0.5.

Q2: What's the difference between 95% and 99% confidence?
A: 99% confidence requires a larger sample but provides more certainty that results reflect the true population.

Q3: How does population size affect sample size?
A: For small populations, the required sample size reduces because you're sampling a larger fraction of the total.

Q4: When should I use a different formula?
A: For continuous variables or comparing groups, different formulas are needed that account for standard deviation and effect size.

Q5: What if my expected proportion is very small?
A: For rare events (p < 0.1), you may need specialized methods like Poisson approximation.